\subsetneqThe symbol \subsetneq is used to denote a proper subset relation where one set is a subset of another but not equal to it. In other words, if A \subsetneq B, then all elements of A are in B, but B contains at least one element not in A.
Set A is a proper subset of set B, meaning A is contained within B but is not equal to B.
A \subsetneq BThe set \{1, 2\} is a proper subset of \{1, 2, 3\} because it does not contain the element 3.
\{1, 2\} \subsetneq \{1, 2, 3\}Indicates that set X is a proper subset of set Y, implying Y has additional elements not found in X.
X \subsetneq Y